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A Distributed Computing Method Integrating Improved Gradient Projection for Solving Stochastic Traffic Equilibrium Problem

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Abstract  

This paper presents two novel algorithmic frameworks to address the logit-based stochastic user equilibrium traffic assignment problem (SUE-TAP). Following the different variant of the gradient projection (termed as GP2) algorithm, we propose an improved GP2 algorithm (IGP) for the SUE-TAP. This study initially presents a smart approach for determining the allocation of more or less effort to specific origin–destination (OD) pairs. Subsequently, the TAP can be decomposed by different OD pairs, whereas the proposed IGP algorithm is designed based on the serial scheme (i.e., the Gauss–Seidel method). Therefore, a new parallel algorithm P-IGP is proposed, which integrates the block coordinate descent (BCD) method and the IGP algorithm. In specific, the independent OD pairs can be separated into several blocks, and the OD-based restricted subproblems within each block can be solved in parallel. Then, we outline the entire process of implementing the P-IGP algorithm to address the SUE-TAP. Several numerical experiments are conducted to verify the proposed algorithms. The results reveal that the proposed IGP algorithm demonstrates significantly speeder convergence in comparison to the traditional GP2 algorithm, achieving a remarkable acceleration of approximately 12%. Furthermore, the performance of the P-IGP algorithm surpasses that of the proposed IGP algorithm, and it can further achieve a notable 4–5-fold enhancement in convergence efficiency.

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Data Availability

The network data used in this study are publicly available, and it is accessible on the website: https://github.com/bstabler/TransportationNetworks.

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Funding

This study is supported by the Key Project (No. 52131203) of National Natural Science Foundation of China.

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing, China

    Honggang Zhang, Zhiyuan Liu, Yicheng Zhang, Weijie Chen & Chenyang Zhang

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  1. Honggang Zhang
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  2. Zhiyuan Liu
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  3. Yicheng Zhang
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  4. Weijie Chen
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  5. Chenyang Zhang
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Contributions

Conceptualization: Honggang Zhang and Zhiyuan Liu; Methodology: Honggang Zhang, Zhiyuan Liu, and Yicheng Zhang; Formal analysis and investigation: Honggang Zhang, Weijie Chen, and Chenyang Zhang; Writing-review and editing: Honggang Zhang, Zhiyuan Liu, and Yicheng Zhang; Funding acquisition: Zhiyuan Liu; Writing-original draft: Honggang Zhang. All authors reviewed the manuscript.

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Correspondence to Zhiyuan Liu.

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Zhang, H., Liu, Z., Zhang, Y. et al. A Distributed Computing Method Integrating Improved Gradient Projection for Solving Stochastic Traffic Equilibrium Problem. Netw Spat Econ (2024). https://doi.org/10.1007/s11067-024-09617-3

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